Despite extensive research for more than 200 years, the experimental isolation of monatomic sulphur chains, which are believed to exhibit a conducting character, has eluded scientists. Here we report the synthesis of a previously unobserved composite material of elemental sulphur, consisting of monatomic chains stabilized in the constraining volume of a carbon nanotube. This one-dimensional phase is confirmed by high-resolution transmission electron microscopy and synchrotron X-ray diffraction. Interestingly, these one-dimensional sulphur chains exhibit long domain sizes of up to 160 nm and high thermal stability (~800 K). Synchrotron X-ray diffraction shows a sharp structural transition of the one-dimensional sulphur occurring at ~450-650 K. Our observations, and corresponding electronic structure and quantum transport calculations, indicate the conducting character of the one-dimensional sulphur chains under ambient pressure. This is in stark contrast to bulk sulphur that needs ultrahigh pressures exceeding ~90 GPa to become metallic.